Formula
Initial n₀ = z²p(1−p) ÷ e²; finite-population n = n₀ ÷ [1 + (n₀−1)/N]
p is the expected proportion, e is the desired half-width, and N is the optional dataset size.
What the result means
Use the main result together with the supporting bounds, counts, or capacity figures. The estimate is only as reliable as the input definitions, sampling process, and operating assumptions.
The formula assumes a random sample and independent observations. Clustered entities or repeated rows may require a larger design-adjusted sample.